# Efficiency Measurement - PowerPoint PPT Presentation

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William Greene Stern School of Business New York University. Efficiency Measurement. Lab Session 2. Stochastic Frontier Estimation. Application to Spanish Dairy Farms. N = 247 farms, T = 6 years (1993-1998). Using Farm Means of the Data. OLS vs. Frontier/MLE. JLMS Inefficiency Estimator.

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Efficiency Measurement

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#### Presentation Transcript

William Greene

New York University

## Lab Session 2

Stochastic Frontier Estimation

### Application to Spanish Dairy Farms

N = 247 farms, T = 6 years (1993-1998)

### JLMS Inefficiency Estimator

FRONTIER ; LHS = the variable

; RHS = ONE, the variables

; EFF = the new variable \$

Creates a new variable in the data set.

FRONTIER ; LHS = YIT ; RHS = X ; EFF = U_i \$

Use ;Techeff = variable to compute exp(-u).

Confidence Intervals for Technical Inefficiency, u(i)

Prediction Intervals for Technical Efficiency, Exp[-u(i)]

Prediction Intervals for Technical Efficiency, Exp[-u(i)]

### Similar, but differentwith a crucial pattern

The Dreaded Error 315 – Wrong Skewness

### Cost Frontier Command

FRONTIER ; COST

; LHS = the variable

; RHS = ONE, the variables

; EFF = the new variable \$

ε(i) = v(i) + u(i) [u(i) is still positive]

### Normal-Truncated NormalFrontier Command

FRONTIER [; COST]

; LHS = the variable

; RHS = ONE, the variables

; Model = Truncation

; EFF = the new variable \$

ε(i) = v(i) +/- u(i)

u(i) = |U(i)|, U(i) ~ N[μ,2]

The half normal model has μ = 0.

### Observations

• Truncation Model estimation is often unstable

• Often estimation is not possible

• When possible, estimates are often wild

• Estimates of u(i) are usually only moderately affected

• Estimates of u(i) are fairly stable across models (exponential, truncation, etc.)

### Truncated Normal Model ; Model = T

Truncated Normal vs. Half Normal

### Ranking Observations

CREATE ; newname = Rnk ( Variable ) \$

Creates the set of ranks. Use in any subsequent analysis.